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Fundamental Component in encryption systems
Elliptic Curves (ECs) have shown their efcacy as a safe fundamental component in encryption systems, mainly when used in Pseudorandom Number Generator (PRNG) design. This paper proposes a framework for designing EC-based PRNG and maps recent PRNG design techniques into the framework, classifying them as iterative and non-iterative. Furthermore, a PRNG is designed based on the framework and verifed using the National Institute of Standards and Technology (NIST) statistical test suite. The PRNG is then utilized in an image encryption system where statistical measures, diferential attack measures, the NIST statistical test suite, and system key sensitivity analysis are used to demonstrate the system’s security. The results are good and promising as compared with other related work. Chaos-based techniques gained much attention because of their sensitivity to system parameters and initial conditions. While some techniques added extra parameters to chaotic systems to increase their sensitivity and system key length1–3, others generated dynamic S-box using either Henon map4 or logistic-sine map5, or gen erated random keystream using quantum logistic map6. On the other hand, non-chaos-based systems gained attention from the diversity of components that can be combined to achieve comparable security strength. For example, such systems can utilize the complex details of fractals in the PRNG process7,8, use Linear Feedback Shif Register (LFSR) in image encryption9, perform permutation and substitution using Feistel networks10, or apply a DNA encoding process of image pixels11. Moreover, two assessment measures were developed for the performance of various chaotic and non-chaotic based permutation techniques12. A summary of several encryp tion system confgurations, based on chaotic and non-chaotic generators, was proposed by Ref.13 demonstrating the efect of each confguration on system security.ECs are utilized because of the difculty of the Discrete Logarithm Problem (DLP) and the ability to achieve high-security strength using a smaller key length than other public-key techniques. For instance, designing an authenticated encryption scheme for message mapping on EC14,15, generating discrete chaotic sequences using the EC-based linear congruential method16, using isomorphic elliptic curves in generating S-boxes17, improving the ElGamal encryption technique by solving data expansion issue18,19, or utilizing the Dife–Hellman key exchange protocol and EC point addition in image encryption20 are among the techniques that utilize ECs.The main contributions of this paper are summarized as follows. First, a novel generalized framework for EC-based iterative and non-iterative PRNG is proposed and verifed using recent literature. With the help of this framework, a simple PRNG based on ECs is designed using one EC point addition operation and two trunca tions. In addition, an image encryption system combining chaos and number theory is designed by utilizing the proposed PRNG. Finally, the PRNG and encryption system are evaluated using well-known standard criteria and they demonstrated good results.